Rotor for turbo-blowers, centrifugal pumps and the like



March 21, 1933.

H. nNoKUTY ET AL.

KOTOR FOR TURBOBLOWERS, CENTRIFUGAL PUMPS, AND THE LIKE Filed June 20, 1930 4 Sheets-Sheet 1 4 Sheecs--Shee'cl 2 March 21, 1933. H. lNoKUTY Er AL HOTR FOR TURBOBLOWERS, CENTRIFUGALPUMPS, vAND THE LIKE Filed June 2o, 1930 uvemcozs: H 4 /noK bl QC 3. haga@ K Q @513 Miou/Legs: 77M /L March 21,-1933. H. lNoKUrY Er AL 1,902,406

CENTRIFUGAL PUMPS, AND THE LIKE ROTOR FOR TURBO-BLOWERS,

Filed June 20, 1930 4 Sheets-Sheet 5 500 Hg. 5a... I 005325 March 21, 1933. H. INOKUTY Er AL ROTOR FOR TURBO-BLOWERS, CENTRIFUGAL PUMPS, AND THE LIKE Filed June' 20, 1930 4 Sheets-Sheet 4 Patented Mar. 21, 1933 iJNl'rED STATI-:s

PATENT OFFICE HABUHISA INOKUTY, OF HONG'O-XU, TOKYO, .AND ZY'UNKITI NAGAOKA, 0F SHITAYA-KU, TOKYO, JAPAN ROTR IFOB. TURBO-BLOWERSQ CENTRIFUGAL PUMPS AND THE LIKE Application led .Tune 20, 1930, Serial No.

This invention relates to improvements in or relating to rotors of turbo-blowers, centri'- fugal pumps and the like, made up of two or more disks coupled elastically by means of vanes. The object of the invention is to obtain astrong and eiicient rotor while reducing the greatest circumferential stress at the inner edge of the cover disk to the value equal or almost equal to that in the main disk at the point situated at the same radial distance as the inner edge near the opening in the cover disk, and the stress in the material of the vanes as small as possible, by making the radial displacements and the stresses at the points of the same radial 'distances in both disks as nearly equal as possible. And especially by making equal or similar the thicknesses of the main and cover disks of the'rotor of a turbo-blower or centrifugal pump, and by fitting on the innermost radial part of the cover diskwhich has the larger central opening, a proper shrinkage ring or rings to produce such -a proper inward pressure that, when the thicknesses are equal, the cover disk carrying half the material of the elastic coupling of the disks as the load due to the centrifugal force, will undergo the same radial displacement as the main disk; and that, when the thicknesses are not equal but approximately so, the cover disk carrying a part of the material of coupling in proportion to the thicknesses of disks will undergo almost the same radial displacement as the main' disk.

In the accompanying drawings Fig. l is a sectional elevation of an example of a six stage turbo-blower iitted with the rotors of our invention. Fig. 2 is a similar sectional elevation of an example of an eight stage 40 turbo-blower of the same capacity as that shown in Fig. 1, but fitted with ordinary rotors. Fig. Sa'represents in full lines a half radial section of one practical example of the rst stage rotor of our invention with shrinkage rings shown in Fig. 1 with its di- 462,654, and in Japan November 2, 1929.

mensions in millimeters, and showing in chain lines a similar half section of the cover plate of the rotor of ordinary design as shown in Fig. 2, so as to compose a complete rotor when it is fitted to the main disk of the rotor represented in full lines in Figs. 2 and 3a, with the vanes of a properly increased Width as shown in Fig. l. Fig. 3b represents a sectorial part of a rotorI as in Fig. 3a, without cover plates, showing the shape and the arrangement of the vanes. Fig. 3o represents in full lines the curves of the radial and circumferential stresses inkilogrammes per square centimeter in the main and the cover disks of the rotor of our invention shown in Figs. l and 3a against the abscissae of the radial distance of the pointin rotor, when it revolves at a speed of 5850 revolutions per minutegand there is also shown in chain lines the similar curves of the stresses in the rotor of ordinary design represented also in Figs. 2 and 3a composed of a cover plate represented in chain lines joined to the main disk with vanes of a greater width as shown in Fig. 3a when it revolves at a speed of 4840 revolutions per minute. Fig. 4 represents a radial section similar to Fig. 3a partly broken away of the rotor of our invention. Fig. 5 represents a section similar to Fig. 3b, showing only a sectorial part, of the rotor represented in Fig. 4r, with cover plate removed to show the shape and the number of the vanes. Fig. 6 represents an axial view of an elementary part of the main disk bounded by two radial planes making a small angle of 8H passing through the axis of rotation of the rotor, and two concentric cylindrical surfaces with their axes coinciding with the axis of rotation of the rotor and their radii differing by a small amount 81'. Fig. 7 is a section on line OX of the same elementary part as shown in Fig. 6. Fig. 8 is a diametrical section similar to Figs. 3a and 4 of a conventional torml of rotor consisting of one main disk and two cover disks each having a relatively large central opening for the admission of gas and showing the application of the invention thereto. Similar characters of references indicate corresponding parts throughout the figures q 5 and referring now to the same:

A in Fig. 1 and A in Fig. 2 are the rotors of turbo-blowers mounted on the shafts H and enclosed in the casings M with partition walls P defining ai plurality of separate chambers UU, in each of which is situated a rotor A or A', a guide vane ring B, and a return passage C. In Figsfl and 2, when the shaft H is rotated by a suitable prime mover, which is not shown in the figures coupled to the shafts at the end H, air or gas will be sucked in by the rotational action of the rotors from the inlet opening S of the casing M, and passes into the rotor from the suction open- 20 ing E of the first rotor A or A', and is decoupling, or vanes in case of the rotor of a turbo-blower, be proportional to the difference of radial displacements of the main and the cover disks, el and e2; whilst the factor of proportionality G, is a certain function of the radial distance 7", to be determined by the geometrical configuration and the elastic properties of the coupling or vanes. The

force may, therefore, be expressed as follows: A

livered finally, through the last annular passage Q of the last guide vane ring, to the delivery opening D of the casing M.

In considering the equilibrium of the two rotating disks, such as in the case of the rotors of turbo-blowers, the assumptions adopted ordinarily are the stress distribution in the disk is considered as uniform in the direction parallel to the axis of rotation, (2) the width 'of the disk in the direction parallel to the axis of rotation changes very gradually, and (3) points situated at equal radial distances at rest will remain also at equal radial distances from the axis of rotation when running. To these assumptions ordinarily adopted we add furthermore the following which are necessary for the new method of analysis lirst introduced by the inventors: (4) The elastic force caused by the coupling of the two disks is assumed to .be distributed uniformly on the points situated at the same radial distances from the center of rotation of the rotor, and (5) the direction of the forces caused exerted on the discs by the coupling are assumed to be radial. v 60 In Fi 4 and 5, the main disk is designated by 1 an the cover by 2. a is the outermost radius which is the same for both disks; b is the innermost radius of the cover disk, disre` garding the packing ring of the rotor. As- 65 sume that the force caused by the elastic where f, and fri, principal circumferential and radial stresses in the main disk,

fz' and frz, principal circumferential and radial stresses in the cover disk,

y1 and y2, axial thicknesses of the main and cover disks,

el and e2, radial displacements of the points in the main and the cover disks,

fr, radial distance of the point in the disks,

as shown in Figs. 4 and 5,

0, angle measured in the direction of rotation,

GU), radial outward force exerted by the cover disk on the unit area of the normal surface of the main disk through vanes, when (e2-e1) is unity,

p., density of material of disks and vanes, that is, specific gravity divided by g,

w, angular velocity of rotation of disks,

n, number of vanes,

z, width of vane, as shown in Fi 4,

t, thickness of vane, as shown in ig. 5,

y, angle of vane, as shown in Fig. 5,

, function of 1', its value being a fraction between zero and unity, and the part a of vane being assumed to have the eHect of its centrifugal force on the cover disk, whilst the part (l-) z on the main disk as shown in Fig. 4.

Putting in the equation of equilibrium now obtained the stresses given by the following equations de e jo- V'l and where E=Youngs modolus of elasticity,

. v= Poissons ratio,

We have for the equation of the displacement of the main disk @enana (111111 1 1-2 Where A=,un2. For the cover disk, We have a similar equatlon:

Where Z=ntz/21r sin y.

When the thicknesses y1 and y2 of the tWo disks are of a constant ratio 7c, that is y1=g/c2 for every radial distance, the Equations (1) and (2) Will be identical if (1-)/?/1=C/?/2 or =1/(c| 1). In such a mode of dividing up the vanes, all the axial dimensions of the disks Will be identical all over the disks. When the thicknesses are not similar, there will be always only one method of dividing up the vanes, so as to make the displacements nt: 211' sin ryzof the virtual disks equal. 'In such a case, We must have @sans @man elweZ-e (Zr-d1 dr drzddrz-drz and.

fr1=fr2=fr- Utilizing these, We have from (1) and (2) d 1- 2 d-+=ST= E fr (3) Where 1-1' 1 l 1 1i lf/ 2 S E AZ y1+y2 y1d7` y2 dT (4) 1 2 1 annie TF- E y1 d?" y2 dr (5) The Equation (3) will be integrated easily, and will have the form Where a is a constant of integration. Putting this in Equations (1) or (2)', and of course making G=0, We have cal.

tions.

l S *rldisJf rs r2 K+ S+ rs f2s T (7) two vililtual disks are i? a constant raticof k, Where With t eir equations o dis lacementsi enti- .v

So We have their di'slplacements el and 2)(1) =dS+S Ti-i-Z (Zh-tm S (8) e2, that is, the solutions of the equations, dr y1 T y2 dr 71 equal; if We have the same boundary condidt T dy2 (1 v)T Generally We have the same outer- 9(7): '-57,72@ 1. .'l

most radii for the both disks in rotors of 1*2 1 1; ordinary construction, but the innermost -fhM-n a (9) radii of the holes are dilerent, being generr ally larger in the cover than in the main disk. S dp dq The boundary conditions in the innermost 15": 75 P(7)=; 9,(7)

edges of the both disks are, therefore, different. If We put on a proper shrinkage ring or rings R at the innermost edge of the cover disk, giving a proper inward pressure, the boundary condition at the inner edge of the cover may be made equal to that at the point Solving Equation (7) We can determine the method of dividing and the vanes so as to make e1=e2. After We have thusknown the function giving the method of separation of the Whole disk into tvvo virtual disks, We can easily calculate the necessary shrinkage ring or rings to be fitted on the innermost edge of the cover disk so as to make the disllO placements e1, e2 and the stresses in the both virtual disks equal. Y

The complete actual rotor made up of the virtual disks coupled elastically by the vanes is, however, different from those virtual ones. The actual rotor, being two or more rotating disks elastically coupled, will assume in revolution a position of the minimum strain energy under the condition of stable equilibrium. The function l; will be such that satisfies this condition, and it is not easy to find the actual form of the function lg, excepting in some special cases. There will not be, however, much error in assuming as given by 1/ (7c-ll) in case of similar disks, and that given b Equation (7) in case of dissimilar disks, i the material of the vanes is not very much in comparison with that of the both disks in all. And further when the disks have similar thicknesses, the error is very small; and, moreover, when they are ofthe same thickness, but have only a different in- .minute the stresses and the nermost diameter of the holes, k will be unity and ,willbe l, it is not diiiicult to prove that the position of the stable equilibrium giving the minimum strain energy of the complete rotor will be that due to the partition of the vanes by C equal to 1/2, or just the same as in the case of virtual disks separated by the function =1/(k+1)=1/.

It will be easily supposed that, even in the case of dissimilar disks, the difference of the radial displacement of both disks with the proper shrinkage ring or rings as calculated for the two virtually separated disks according to the method invented by the inventors,

are very small compared with that of the da. hbrida unimi 1-2 disks without shrinkage. In Figs. 3a and 3b, part sections of an ordinary rotor A are represented, consisting of dissimilar disks 1, indicated in full lines, and 2, indicated in chain lines, and Fig. 3c gives in chain lines the stresses in the two disks when running at a speed of 4840 revolutions per minute, calculated by the ordinary method, assuming vanes as the load on the main disk and the cover without vanes; that is, =0 and G=0.

The curves represented in full lines in Fig. l3c are the stresses for the virtual disks obtained by dividing up, so that ':3/(44-3), the rotor A represented in Fig. 1 and Fig. 3a in full lines, and with the cover similar to and 3A; as thick as the main disk having shrinkage rings R represented in Fig. 3a. according to this invention when they are run at a speed higher than 5580 revolutions per yAs has been explained previously, displacements inV the disks of an actual rotor will not bemuch different from those calculated and represented in full lines in Fig. 3c for the two virtual disks. It will be noticed that the circumferential stress f02 in the cover disk of the ordinary rotor seems to be very great at its innermost edge, whilst the radial stress frz is nil, and very small all over in the cover. The part of the cover, therefore, near the riveting holes for fastening the vanes will be liable to be subjected to a heavy stress of about three times the large circumferential stress 02 in the cover. By aid of our invention o strengthening the cover with a proper shrinkage ring or rings R, the circumferential stress fg in the cover will be reduced equal or almost equal to that in the main disk as shown in Fig. 3c even at a higher speed, and moreover the radial stress frz in the cover will be increased equal or almost equal to that in the main disk fm. The heavy stress, therefore, in the neighbourhood of-the holes for riveting vanes will be greatly reduced. Thus greater safety and reliability of the rotor in every respect is attained even at a higher speed.

With this increased speed of revolutions from 4840 to 5580, the number of the stages of the turbo-blower in consideration is reduced from eight to six as shown by comparison ot Figs. l and 2, which was simply eected by modifying the cover only, but not the 'main disk. With the proper modifications of both the cover and the main disks suitable to carry the new invention into practice, a further reduction in the number of the `stages will be effected.

AVhen the disks are similar in thickness the Equation (2) will be reduced to Equations (l) and (2) will be e1= 7n 7l) (lo) @2=(T)'+alf(, T) (11) where is a certain function of radial distance 7', and lp of and r, both of which will depend on the forms of the Equations (l) -and (2).` From these equatins of displacements, we can derive the equations oi the principal radial and circumferentia stresses, and they are ffl:

je.: 1 ,2l-w) am, a] 13) fr2= 1 E .lam kas, o] 14) where F rom these equations of displacements and stresses, it will not be diiiicult to find the form of the function satisfying the condition of the minimum strain energy; and it is found that in the case where the disks are similar in thickness, the form of previously determined for the separation into two virtual disks having equal displacements is not much diiferent from that giving the minimum strain energy inthe complete actual disk. And further it is deduced that when the disksare equal in thickness, the constant value of =1/ will be that giving to both the virtual and actual disks equal displacements and stresses, giving practically the least stress in the' material of the elastic coupling, that is vanes, of the disks.

From the foregoing it is obvious that the invention. may be as well applied to a rotor of the type illustrated in Fig. 8 consisting of three discs, the two cover discs of which are provided with central inlet openings. In applying the foregoing calculation to the rotor to find proper shrinkage rings to be fitted to the cover discs, assume that half the thickness of the main disc belongs to a cover disc when the passages on both sides of the main discs are of equal width, as shown in Fig. 8.

We claim.

1. A rotor for turbo-blowers, centrifugal pumps and the like including vanes, discs coupled together elastically hy said vanes,

one of said discs having an lnner opening,

and a shrinkage ring fitted on the innermost radial part of said disc and rendering the displacements and strees in both discs substantially equal.

2. A rotor for turbo-blowers, centrifugal pumps and the like including vanes, a c'entral disc and two outer discs, said outer discs having inner openings, the central disc being coupled elastically with each of the outer discs by said vanes, and a shrinkage ring fitted on the innermost radial part `of each of said outer discs and rendering the displacements and stresses in the three discs substan-l tially equal.

In testimony natures.

HARUHISA INOKUTY. ZYUNKITI NAGAOKA.

whereof they aix their sig. 

